Scientists in the Section on Biomedical Stochastic Physics (SBSP) devise quantitative theories, develop methodologies, and design instrumentation to study biological phenomena whose properties are characterized by elements of randomness in both space and time. The research focuses on developing quantitative theories applicable to in vivo quantitative optical spectroscopy and tomographic imaging of tissues. SBSP researchers design and conduct experiments and computer simulations to validate theoretical findings. Many biological tissue components such as collagen, muscle fibers, keratin, retina, and glucose possess polarization properties. Depolarization of the polarized light depends strongly on the bulk optical properties of the tissue (absorption and scattering coefficients) and optical anisotropy. SBSP scientists map the degree of polarization to visualize structural information about skin, and study the propagation of polarized light in tissue and tissue-like phantoms and the possible application of polarized light for tissue diagnostics. Mapping the degree of polarization may carry valuable information about the superficial and subsurface structures of the skin and other tissues, and may contain information that one cannot observe visually or photographically. In many cases, enhancing the subsurface structures which may be distorted in the procedure of polarization degree patterning improves the images. For this purpose, a statistical analysis and methodology of noise filtering enhances the hidden structures and also estimates the characteristic sizes and directionality of possible structures. Deep-tissue optical imaging is of particular interest, as the equipment costs are lower than for competing technologies such as MRI. For this purpose, the development of novel contrast agents with near-infrared fluorescence is especially important. Semiconductor nanocrystals of CdMnTe/Hg were grown in aqueous solution and then coated with a biologically compatible surface. The nanocrystals were approximately 5 nm in diameter and have a broad fluorescence peak in the NIR (770 nm). Nanocrystals were injected either subcutaneously or intravenously into athymic NCR NU/NU and C3H/HENCR MTV mice and then excited with a spatially broad 633 nm source; the resulting fluorescence was captured with a sensitive CCD camera. We have demonstrated that the nanocrystals are a useful angiographic contrast agent for vessels surrounding and penetrating a murine squamous cell carcinoma in a C3H mouse. Preliminary assessment of the depth of penetration for excitation and emission was done by imaging a beating mouse heart, both through an intact thorax and after a thoracotomy. The temporal resolution associated with imaging the nanocrystals in circulation has been addressed, and the blood clearance for this contrast agent has also been measured. Fluorophore lifetime imaging is a promising tool for early detection of tumors. The lifetime (time for an electron to return from excited state to initial state) of a fluorophore can vary in response to changes in the immediate environment such as temperature, pH, tissue oxygen content, nutrient supply, and bioenergetic status. The heterogeneity in tumor vascularity can be seen as changes in pH and temperature. An ATCSPC fluorescence lifetime measurement system was established that was suitable for measuring the fluorescence lifetime in the experimental context of the application. Data was collected regarding the behavior of decay shapes with respect to the position of the fluorophore and the surrounding pH value, and correlated with theoretical simulations, where satisfying results from this step should be the basis for the analytical solutions of the inverse problem. The next steps are to scan a sample in the XY plane and synchronize the scanning coordinates with the TCSPC system, thus obtaining a 2D lifetime map from every sample. This 2D map will then be translated into a pH values map according to scaling measurements. Once the first analytical solutions are ready to be implemented, in vivo measurements will take place and the results will be compared with histopathological analysis. We have developed and established the use of three non-invasive techniques to study angiogenesis in KS patients undergoing an experimental anti-KS therapy: thermography, laser Doppler imaging (LDI), and multi-spectral imaging. The KS studies are ongoing clinical trials under three different NCI protocols. Images are recorded of the lesion and compared to normal skin either adjacent to the lesion or on the contralateral side. Measurements were obtained prior to therapy and after receiving a regimen of liposomal doxorubicin and interleukin-12 for 18 and 42 weeks. Scientists in SBSP use three non-invasive imaging techniques for the KS and CRPS-I clinical protocols. Multi-spectral images show local variations in skin analyte concentrations such as oxy- and deoxy-hemoglobin and blood volume after processing. LDI measures the blood velocity of small blood vessels, which generally increases as blood supply demand increases. Combining multi-spectral imaging and LDI allows us to determine changes in blood volume, oxygenation state and blood velocity of the microvasculature and location of the abnormality. These two techniques are limited by their ability to only detect vasculature information near the skin?s surface. The third imaging technique, thermography, provides the temperature as a means of assessing blood flow. A higher temperature represents the skin superficial to veins that are involved in the active transport of blood. Thermographic patterns in medical diagnostic applications may be related to increased blood flow associated with increased metabolic activity. To study the network formation of endothelial cells (ECs) in an extracellular matrix (ECM) environment, we have devised an EC aggregation-type model based on a diffusion-limited-cluster-aggregation model (DLCA), where clusters of particles diffuse and stick together upon contact. We use this model to quantify EC differentiation into cord-like-structures by comparing experimental and simulation data. Approximations made with the DLCA model, when combined with experimental kinetics and cell concentration results, not only allow us to quantify cell differentiation by a pseudo diffusion coefficient, but also measure the effects of tumor angiogenic factors (TAF) on the formation of cord-like-structures by comparing experimental and simulation data. Approximations made with the DLCA model, when combined with experimental kinetics and cell concentration results, not only allow us to quantify cell differentiation by a pseudo diffusion coefficient, but also measure the effects of tumor angiogenic factors (TAF) on the formation of cord-like structures by ECs. We have tested our model by using an in vitro assay, where we record EC aggregation by analyzing time-lapse images that provide us with the evolution of the fractal dimension measure through time. We have shown that the shape, kinetic aggregation, and fractal dimension of the EC aggregates fit into an in vitro model capable of reproducing the first stage of angiogenesis. We conclude that the DLCA model, combined with experimental results, is a highly effective assay for the quantification of the kinetics and network characteristics of ECs embedded in ECM proteins.